Chryssis Michael's penalty was saved in the 21st minute and Konstantinos Makridis struck the post 12 minutes from time as they failed to make the breakthrough against Iceland, who earned their first point of the campaign with the draw.
Cyprus dominated the play, and there were early chances for Dimitris Christofi and Efstathios Aloneftis, but they failed to test Stefan Magnusson in the Iceland goal. However, the goalkeeper clearly kept his focus as he got down low to his left to push Michael's penalty aside after Andreas Avraam was fouled by Kristjan Orn Sigurdsson.
Iceland launched a rare attack just after the half-hour mark, but Heidar Helguson's long-range effort failed to find the target before Antonis Georgallides held a shot from Birkir Mar Saevarsson. Just before half-time, Avraam's close-range effort was parried by Magnusson.
Christofi had a great chance for Cyprus at the start of the second half, but blazed the goal over from close range, and moments later Helguson failed to find the target for Iceland.
After Makridis struck the post, Cyprus launched another assault on the Iceland goal in the final ten minutes, but efforts from Jason Demetriou and Konstantinos Charalambidis were dealt with as Iceland held on for the point.